S. Schmauder

Composite parameters and mechanical compatibility of material joints

The elastic behaviour of a bimaterial interface with interfacial cracks, misfit dislocations and interfacial thermal stresses can be described in a simple manner by using the com posite parameters α and β, and the effective modulus of elasticity E*, assuming a plane deformation of ideally bonded isotropic materials. A coefficient KT for the thermally in duced stress intensity at the interface serves as a measure of the mechanical compatibility of two bonded materials. An examination of these parameters for many composite materials shows that the values of the composite parameters α and β are limited to a nar row range and that the material transition can be classified into six groups with regard to their mechanical compatibility.

Modeling of metal matrix composites by a self-consistent embedded cell model

The limit flow stresses for transverse loading of metal matrix composites reinforced with continuous fibers and for uniaxial loading of spherical particle reinforced metal matrix composites are investigated by recently developed embedded cell models in conjunction with the finite element method. A fiber of circular cross section or a spherical particle is surrounded by a metal matrix, which is again embedded in the composite material with the mechanical behavior to be determined iteratively in a self-consistent manner. Stress-strain curves have been calculated for a number of metal matrix composites with the embedded cell method and compared with literature data of a particle reinforced Ag-58vol.%Ni composite and for a transversely loaded uniaxially fiber reinforced Al46vol.%B composite. Good agreement has been obtained between experiment and calculation and the embedded cell model is thus found to represent well metal matrix composites with randomly arranged inclusions. Systematic studies of the mechanical behavior of fiber and particle reinforced composites with plane strain and axisymmetric embedded cell models are carried out to determine the influence of fiber or particle volume fraction and matrix strain-hardening ability on composite strengthening levels. Results for random inclusion arrangements obtained with self-consistent embedded cell models are compared with strength- ening levels for regular inclusion arrangements from conventional unit cell models. It is found that with increasing inclusion volume fractions there exist pronounced differences in composite strengthening between all models. Finally, closed-form expressions are derived to predict composite strengthening levels for regular and random fiber or particle arrangements as a function of matrix hardening and particle volume fraction. The impact of the results on effectively designing technically relevant metal matrix composites reinforced by randomly arranged strong inclusions is emphasized.

Some aspects of the mechanical strength of ceramic/metal bonded systems

Exploratory studies of the strength of ceramic/metal bonded systems have been conducted, using Al2O3Nb as a model. The investigation reveals two important issues: duality in the effect of metal plasticity and important effects of edges. Experiments demonstrate that metal plasticity can be either beneficial, due to plastic blunting of interface cracks, or detrimental because of residual stresses created around cracks in the ceramic. Calculations establish that edge stress concentrations arise in bonded systems, due to mismatch in elastic properties, causing an enhanced driving force on small edge cracks. Edge dominated failures are thus deemed to have major importance in bonded systems.

Embedded atom potential for Fe-Cu interactions and simulations of precipitate-matrix interfaces

A new empirical interatomic potential of the embedded atom type is developed for the Fe-Cu system. The potential for the alloy system was constructed to reproduce known physical parameters of the alloy, such as the heat of solution of Cu in Fe and the binding energy of a vacancy and a Cu atom in the matrix. The potential also reproduces first-principle calculations of the properties of metastable phases in the system. This atomic interaction model was used in simulation studies of the interface of small coherent Cu precipitates in and of dislocation core structure. The phase stability of the body-centred cubic Cu precipitates was also analysed.

Continuum Mesomechanical Finite Element Modeling in Materials Development: A State-of-the-Art Review

Advanced finite element techniques for the simulation of materials behavior under mechanical loading are reviewed. Advantages, limitations and perspectives of different approaches are analyzed for the simulation of deformation, damage and fracture of mate

Transverse strength of metal matrix composites reinforced with strongly bonded continuous fibers in regular arrangements

Abstract The composite limit flow stress for transverse loading of metal matrix composites reinforced with a regular array of uniform continuous fibers is calculated using the finite element method. The effects of volume fraction and matrix work hardening are investigated for fibers of circular cross section distributed in both sqyare and hexagonal arrangements. The hexagonal arrangement is seen to behave isotropically with respect to the limit stress, whereas the square arrangement of fibers results in a composite which is much stronger when loaded in the direction of nearest neighbors and weak when loaded at 45° to this direction. The interference of fibers with flow planes is seen to play an important role in the strengthening mechanism. The influence of matrix hardening as a strengthening mechanism in these composites increases with volume fraction due to increasing fiber interaction. The results for a power law hardening matrix are also applicable to the steady state creep for these composites. The influence of volume fraction on failure parameters in these composites is addressed. Large increases in the maximum values of hydrostatic tension, equivalent plastic stain, and tensile stress normal to the fiber-matrix interface are seen to accompany large increases in composite strength.

Experimental and numerical characterisation of in-plane deformation in two-phase materials

The aim of the present work consists in the comparison of in-plane strain fields with out-of-plane displacements in micro-areas of an Ag/Ni-composite after a macroscopic compressive deformation of 8.6%. The in-plane deformations in an Ag/Ni-composite have been analysed experimentally with a high resolution object grating technique and numerically using the finite element method. The out-of-plane displacements were measured with an atomic force microscope (AFM). The development of local strain fields in micro-areas at the surface of an Ag/Ni-composite was simulated numerically using the FE-method in plane strain condition. A real cut-out of the microstructure served as input for the calculation. The out-of-plane displacements determined by AFM measurements were used further to correct the in-plane values of strains evaluated by the object grating technique. The roughness on the surface of the sample was characterised by fractal dimensions and compared with the in-plane strains in the same micro-region.

Failure mechanisms of additively manufactured porous biomaterials: Effects of porosity and type of unit cell

Since the advent of additive manufacturing techniques, regular porous biomaterials have emerged as promising candidates for tissue engineering scaffolds owing to their controllable pore architecture and feasibility in producing scaffolds from a variety of biomaterials. The architecture of scaffolds could be designed to achieve similar mechanical properties as in the host bone tissue, thereby avoiding issues such as stress shielding in bone replacement procedure. In this paper, the deformation and failure mechanisms of porous titanium (Ti6Al4V) biomaterials manufactured by selective laser melting from two different types of repeating unit cells, namely cubic and diamond lattice structures, with four different porosities are studied. The mechanical behavior of the above-mentioned porous biomaterials was studied using finite element models. The computational results were compared with the experimental findings from a previous study of ours. The Johnson-Cook plasticity and damage model was implemented in the finite element models to simulate the failure of the additively manufactured scaffolds under compression. The computationally predicted stress-strain curves were compared with the experimental ones. The computational models incorporating the Johnson-Cook damage model could predict the plateau stress and maximum stress at the first peak with less than 18% error. Moreover, the computationally predicted deformation modes were in good agreement with the results of scaling law analysis. A layer-by-layer failure mechanism was found for the stretch-dominated structures, i.e. structures made from the cubic unit cell, while the failure of the bending-dominated structures, i.e. structures made from the diamond unit cells, was accompanied by the shearing bands of 45°.

3D-finite-element-modelling of microstructures with the method of multiphase elements

Abstract We present a 3D-multiphase element which permits the finite-element-modelling of the plastic deformation of realistic 3D-microstructures. In contrast to conventional ‘singlephase elements’ where the phase boundaries are simulated by element edges, the ‘multiphase element’ can be assigned to different materials when a phase boundary runs across it. The 3D-multiphase element is firstly applied to a simple test geometry. The efficiency of the 3D-multiphase element method is demonstrated by the analysis of a more complex 3D-microstructure. Finally, for a comparison of 2D- and 3D-simulations the stress distribution obtained in the 3D-calculation is compared with the results of a 2D-simulation of a representative intersection of the microstructure.

Computational mesomechanics of particle-reinforced composites

Abstract Numerical models of deformation, damage and fracture in particle-reinforced composite materials, based on the method of multiphase finite elements (MPFE) and element elimination technique (EET), are presented in this paper. The applicability of these techniques for different materials and different levels of simulation was studied. The simulation of damage and crack growth was conducted for several groups of composites: WC/Co hard metal alloys, Al/Si and Al/SiC composites on macro- and mesolevel. It is shown that the used modern techniques of numerical simulation (MPFE and EET) are very efficient in understanding deformation and damage evolution in heterogeneous brittle/ductile materials with inclusions.